George Gray
07/15/2023 · High School

Kevin bought a \( 7 \frac{2}{3} \) inches tall model of the Statue of Liberty. The scale used for the model was \( \frac{2}{3} \) inch \( =4 \) meters. What is the actual height, in melers, of the Statue of Liberty? Explain how you solved the question.

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To find the actual height of the Statue of Liberty, we need to set up a proportion using the scale given in the problem. Given: - The model of the Statue of Liberty is \( 7 \frac{2}{3} \) inches tall. - The scale used for the model is \( \frac{2}{3} \) inch = 4 meters. Let's denote the actual height of the Statue of Liberty as \( x \) meters. We can set up the proportion as follows: \[ \frac{7 \frac{2}{3}}{\frac{2}{3}} = \frac{x}{4} \] Now, we can solve for \( x \) to find the actual height of the Statue of Liberty. Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{7\frac{2}{3}}{\frac{2}{3}}=\frac{x}{4}\) - step1: Simplify: \(\frac{23}{2}=\frac{x}{4}\) - step2: Swap the sides: \(\frac{x}{4}=\frac{23}{2}\) - step3: Multiply both sides of the equation by \(4:\) \(\frac{x}{4}\times 4=\frac{23}{2}\times 4\) - step4: Multiply the terms: \(x=\frac{23\times 4}{2}\) - step5: Evaluate: \(x=46\) The actual height of the Statue of Liberty is 46 meters.

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The actual height of the Statue of Liberty is 46 meters.
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